The observed infall of galaxies towards the Virgo cluster

Monthly Notices of the Royal Astronomical Society, Jun 2010

We examine the velocity field of galaxies around the Virgo cluster induced by its overdensity. We have studied the velocity–distance relation in Virgocentric coordinates using a sample of 1792 galaxies with distances from the tip of the Red Giant Branch, the Cepheid luminosity, the luminosity of type Ia supernovae, the surface brightness fluctuation method and the Tully–Fisher relation. Attention was paid to some observational biases affecting the Hubble flow around Virgo. We estimate the radius of the zero-velocity surface for the Virgo cluster to be within 5.0–7.5 Mpc, corresponding to 17–26° at the mean cluster distance of 17.0 Mpc. In the case of spherical symmetry with the cosmological parameter Ωm= 0.24 and the age of the Universe T0= 13.7 Gyr, it yields the total mass of the Virgo cluster to be within MT= (2.7–8.9) × 1014 M⊙ in reasonable agreement with the existing virial mass estimates for the cluster.

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The observed infall of galaxies towards the Virgo cluster

I. D. Karachentsev O. G. Nasonova Special Astrophysical Observatory of the Russian Academy of Sciences Nizhnij Arkhyz KChR Russia A B S T R A C T We examine the velocity field of galaxies around the Virgo cluster induced by its overdensity. We have studied the velocity-distance relation in Virgocentric coordinates using a sample of 1792 galaxies with distances from the tip of the Red Giant Branch, the Cepheid luminosity, the luminosity of type Ia supernovae, the surface brightness fluctuation method and the TullyFisher relation. Attention was paid to some observational biases affecting the Hubble flow around Virgo. We estimate the radius of the zero-velocity surface for the Virgo cluster to be within 5.0-7.5 Mpc, corresponding to 17-26 at the mean cluster distance of 17.0 Mpc. In the case of spherical symmetry with the cosmological parameter m = 0.24 and the age of the Universe T 0 = 13.7 Gyr, it yields the total mass of the Virgo cluster to be within MT = (2.7-8.9) 1014 M in reasonable agreement with the existing virial mass estimates for the cluster. 1 I N T R O D U C T I O N The gravitational action of the mass of a solitary system of galaxies leads to deceleration of the local Hubble flow. As a result, the line of average velocity of neighbouring galaxies relative to the centre of a cluster (or a group) deviates from the linear Hubble relation, going to negative values at small distances R < R0. Here, R0 denotes the radius of the zero-velocity surface, which separates the galaxy system against the global cosmic expansion. As shown by LyndenBell (1981) and Sandage (1986), in the simplest case of spherical symmetry with the cosmological parameter = 0 the radius R0 depends only on the total mass of a group MT and the age of the Universe T0: Here, G is the gravitational constant. Measuring R0 using the distances and radial velocities of galaxies outside the virial radius of the system Rvir, we can determine the total mass of the system independent of its virial mass estimate. Note that both methods of deriving mass from internal and from external galaxy motions correspond to different linear scales where R0 is roughly four times as large as the virial radius. In reality, galaxy groups and clusters do not have perfect spherical symmetry, and the cosmology with = 0 is not true. Numerous measurements of distances to nearby galaxies obtained recently with the Hubble Space Telescope (HST) have allowed us to investigate the Hubble flow around the Local Group (LG) E-mail: (IDK); (OGN) Nee Kashibadze. and other proximate groups (Karachentsev et al. 2002, 2006, 2009; Karachentsev & Kashibadze 2006). The radii R0 obtained from observations for nearby groups around the Milky Way and Andromeda (the LG), M81, Centaurus A, Maffei and IC 342, NGC 253 (Sculptor filament) and NGC 4736 (Canes Venatici I cloud) are ranged within 0.71.4 Mpc. The average ratio of total-to-virial masses for these six groups, derived from R0 using equation (1) and from Rvir, turns out to be M T/Mvir = 0.60 0.15 (Karachentsev 2005). However, as noticed by Peirani & Pacheco (2006, 2008) and Karachentsev et al. (2007), in a flat universe dominated by dark energy the resulting MT(R0) mass is higher than that derived from the canonical LematreTolman equation (1). In the concordant cosmological model with the term and m as a matter component, equation (1) takes the form MT = 8G2 R03 f 2H(02m) , (2) f ( m) = (1 m (1 m)3/2arccosh 1 . Assuming m = 0.24 and H0 = 72 km s1 Mpc1, which corresponds to T0 = 13.7 Gyr (Spergel et al. 2007), we can rewrite equation (2) as = 2.12 1012 This yields a mass that is 1.5 times as large as that derived from the classic equation (1). This correction leads to a good agreement, on average, between the R0 mass estimates and the virial masses for the above-mentioned galaxy groups. For galaxies around the nearest cluster in Virgo, the expected velocity deviations from the pure Hubble flow (the so-called Virgocentric infall) were regarded in dynamical models by Hoffman, Olson & Salpeter (1980), Tonry & Davis (1981) and Hoffman & Salpeter (1982). These authors note that with the virial mass of the Virgo cluster Mvir 6 1014 M , the radius of the zero-velocity surface around the cluster amounts to 27 (i.e. the infall zone covers nearly 1 steradian of the sky). According to Hoffman et al. (1980), the observed decrease of radial velocity dispersion within the angular distance = [024] from the Virgo centre for 228 galaxies agrees, in the main, with the Virgocentric infall pattern for the cluster mass mentioned above. Tully & Shaya (1984) considered the phenomenon of the infall of galaxies towards Virgo in both the point-mass and distributed-mass models for the cluster with different values of the cosmological parameter and the age of the Universe T0. Using TullyFisher distance estimates for 19 galaxies inside the virial radius of 6 and 14 galaxies outside it, the authors ascertain the expected infall with R0 28. Later, Tonry et al. (2000, 2001) developed a model of the Virgocentric flow based on accurate distance measurements for 300 E and S0 galaxies from surface brightness fluctuations. Their model fits well with the observational data on galaxy distances and radial velocities for the Virgo cluster distance of 17.0 Mpc and its total mass of 7 1014 M . According to their model, our LG has a peculiar velocity of 139 km s1 directed towards the Virgo centre. Teerikorpi et al. (1992) and Ekholm et al. (1999, 2000) examined the Virgocentric flow with different models of density distribution in the cluster and inferred expected relations between velocities and distances of galaxies relative to the cluster centre. Using Cepheid distances to 23 galaxies and TullyFisher distances to 96 galaxies, they concluded that the radius of the zero-velocity surface ranges from 20 to 31, and the total cluster mass is equal to (12) of its virial value. During the last decade, the observational data base on distances to galaxies in a wide vicinity of the Virgo cluster has grown significantly, allowing us to determine R0 and, therefore, the total mass of the Virgo cluster with better accuracy. 2 O B S E RVAT I O N A L S A M P L E S To examine the phenomenon of the Virgocentric flow, we used distance moduli of galaxies from different publications, preferring more precise measurements. The main data sources are listed below. (i) Taking the luminosity of the tip of the red giant branch (TRGB) as a standard is the most efficient and the most universal method to determine distances to nearby galaxies, as it is practically independent of their morphological type. Being applied to galaxy images in two or more photometric bands obtained with the WFPC2 or ACS cameras on the HST, the TRGB method yields an accuracy of distance measurements of 7 per cent, as found by Rizzi et al. (2007). A consolidated list of distances for the Local Volume galaxies is presented in the catalogue of neighbouring galaxies (CNG; Karachentsev et al. 2004). The CNG sample of 451 galaxies has been collected based on two conditions: galaxy distance D < 10 Mpc, if a galaxy has an individual distance estimate; otherwise, galaxy radial velocity with respect to the LG VLG < 550 km s1. Below, we use from the CNG the galaxies with only TRGB or Cepheid distances, supplying these with new TRGB distances from recent publications (Karachentsev et al. 2006; Tully et al. 2006). (ii) The surface brightness fluctuation method (SBF), applying to early-type galaxies, assumes that the old stellar population (RGB) is prevailing in a total luminosity, and the galaxy structure does not suffer from irregularities as a result of dust clouds. Using this approach, Tonry et al. (2001) determined SBF distances to 300 E and S0 galaxies with a typical errors of 12 per cent. This sample is distributed over the whole sky extending to cz 4000 km s1 with a median velocity of 1800 km s1. (iii) Mei et al. (2007) undertook a two-colour ACS/HST imaging survey for 100 early-type galaxies situated in the Virgo cluster core (the ACSVCS project). They derived precise SBF distances to 84 E, S0 galaxies with a typical error of 8 per cent, and revealed the threedimensional (3D) shape of the Virgo cluster to be a slightly triaxial ellipsoid with axis ratios of (1 : 0.7 : 0.5). We expanded the ACSVCS sample with other precise SBF and TRGB distance measurements in the Virgo core made by Neilsen & Tsvetanov (2000) and Caldwell (2006) with ACS/HST and by Jerjen, Binggeli & Barazza (2004) with the Very Large Telescope. This yields the total ACSVCS+ sample of 116 galaxies. (iv) In the wide vicinity of the Virgo cluster, there are 22 galaxies with distances measured by Tonry et al. (2003) using type Ia supernovae (SNIa). This sample is small but has a distance error of only 5 per cent. (v) Based on the Two-Micron All-Sky Survey (2MASS) Selected Flat Galaxy Catalogue (2MFGC; Mitronova et al. 2004), Kashibadze (2008) determined distances to 402 spiral edge-on galaxies with radial velocities <3000 km s1. A multiparametric near-infrared TullyFisher relation was applied to these, yielding a typical distance error of 20 per cent. The zero-point of the luminositylinewidth relation was calibrated by 15 galaxies with Cepheid and TRGB distance measures. (vi) Finally, the former samples of galaxies were supplemented with a compilation of distances by Tully et al. (2008, 2009), which have been obtained from optical (B, R or I band) one-parametric TullyFisher relations. This compilation relies on numerous H I line and photometric observations carried out by Methewson & Ford (1996), Haynes et al. (1999), Tully & Pierce (2000), Koribalski et al. (2004), Springob et al. (2005), Theureau et al. (2006) and other authors. Zero-points of the data were recalibrated by a set of 40 galaxies with known Cepheid and TRGB distances. As a last step, we used also distances from a very large and important SFI++ sample (Springob et al. 2007), which have not been included in the Tully et al. (2009) compilation. In total, we used distance estimates for 941 spiral galaxies whose radial velocities were limited by 3000 km s1. The typical distance error for these is 20 per cent, although there are some cases with much higher errors because of uncertainties of galaxy inclination, the presence of interacting companions or H I profiles of low quality. A substantial overlap between the two last luminositylinewidth samples provides confirmation that their zero-points are the same, and gives rms agreement per measure of 0.40 mag. As seen from fig. 1 of Tully et al. (2008), there is an excellent agreement in distance moduli between the luminositylinewidth and other (Cepheid, TRGB, SBF and SNIa) measures. In particular, for 12 galaxies in our list with both TF and TRGB or SNIa moduli, the mean distance difference is (1.4 1.2) Mpc, while for 20 galaxies with SBF or TRGB moduli the average difference is only (0.2 0.2) Mpc. Following the previous authors (Tully & Shaya 1984; Ekholm et al. 2000), we have formed a composite sample of galaxies limiting their angular separation from the Virgo centre to < 30. We have considered the radio galaxy Virgo A (NGC 4486) to be the physical centre of the cluster as its position is close to the centre of X-ray i: TRGB + Ceph ii: SBF (Tonry) iii: ACSVCS+ iv: SNIa (Tonry) v: TF (IR) vi: TF (opt) emitting gas. The total number of galaxies in this cone volume with apex angle < 30 is 630 the two-dimensional (2D) sample. Limiting the angular separation of galaxies from the Virgo centre introduces some selection effects into the Virgocentric flow analysis. For this reason, we have also used another way to form the observational sample, considering galaxies with spatial distances from the Virgo cluster centre Rvc < 30 Mpc the 3D sample. This approach suffers a drawback too because galaxy distances are measured with errors and their significance is different at the proximate and the distant boundary of the spherical volume (the so-called Malmquist bias). The total number of galaxies in our 3D sample amounts to 1792, and the fractions of diverse subsamples differ significantly from that in the 2D sample. Table 1 presents the summary of observational data that we have used. The first column indicates the type of subsample, and the second gives typical distance errors expressed in magnitudes. Columns 3 and 5 contain the numbers of galaxies in the cone (2D) or in the spherical (3D) volumes. The sample goodness G, defined as G = (N/100)1/2 m1, is a useful parameter that characterizes a statistical weight of a certain sample (Kudrya et al. 2003). Goodness values are indicated in columns 4 and 6. For example, the subsample of galaxies with SNIa distances is scanty but its statistical significance is comparable with that of other samples because of the higher accuracy of distance measurements. As we can see, the galaxy subsample ACSVCS+ has the maximum statistical weight in the 2D set; however, almost all these galaxies are concentrated within the virial radius. In the 3D set, the highest goodness corresponds to the TRGB sample, but its majority is crowded on the nearby side of the examined volume. The last two TF samples exhibit a significant increase in number going from the 2D to the 3D samples, which is caused by the well-known effect of morphological segregation of late-type versus early-type galaxies along the cluster radius. 3 R A D I U S O F T H E Z E R O - V E L O C I T Y S U R FAC E R0 The virial radius of the Virgo cluster Rvir = 1.8 Mpc (Hoffman et al. 1980) corresponds to its angular scale of 6.0, assuming the average distance to the cluster members to be 17.0 Mpc. Radial velocities and distances relative to the LG centroid for 259 galaxies in this zone are represented in the top panel of Fig. 1. Here, precise distances for most of the galaxies were obtained within the special survey ACSVCS with the HST (Mei et al. 2007). The Virgo cluster members, located in the distance range from 14 to 20 Mpc, demonstrate a radial velocity scatter from 800 up to +2300 km s1. Foreground galaxies are scarcely presented on the panel while background objects tend to lie below the linear Hubble regression with the global Hubble parameter H0 = 72 km s1 Mpc1 (Spergel et al. 2007), showing thereby the expected effect of infall into the Virgo cluster from the opposite side. The centroid of galaxies forming the virial column at [17.0 1.8] Mpc, marked by vertical lines, has a mean velocity +1004 70 km s1 versus the expected Hubble velocity of +1224 km s1 at the distance of 17.0 Mpc. This can be explained by a peculiar motion of the LG 220 70 km s1 directed towards Virgo. The dotted and solid S-shaped curves correspond to a Hubble flow perturbed by a point-like mass of 2.7 1014 and 8.9 1014 M (as the limiting cases discussed below) for the line of sight passing exactly through the cluster centre. The distributions of radial velocities and distances for the remaining galaxies of the 2D sample in the close surroundings of Virgo (6 < < 15) and in a distant periphery (15 < < 30) are shown in the middle and bottom panels of Fig. 1. Here, the solid and dotted S-shaped lines, having lower amplitudes, describe the behaviour of the perturbed Hubble flow at angular distances equal to 6 and 15, respectively. These panels display some signs of the infall effect too; however, in front of Virgo, the expected infall is barely seen. Considering a set of such Hubble diagrams with their different amplitudes of S-shaped waves decreasing with the angular distance , we can find the quantity of the cluster mass that fits the observed infall pattern in the best way. However, this approach seems to us to be not transparent enough. In order to determine R0, and the total cluster mass using this, we have converted our observational data into distances and velocities expressed relative to the cluster centre. The top panel of Fig. 2 shows the layout of a galaxy (G) relative to the observer (LG) and the cluster centre (C) with angular separation from the cluster centre. The spatial distance of the galaxy from the centre therefore is Rv2c = Rg2 + Rc2 2RgRc cos . Assuming that the galaxy and the cluster centre are involved in an almost unperturbed Hubble flow (the Hf case) with negligible peculiar velocities, we can state the mutual velocity difference between G and C in projection on to the straight line connecting them as where = + and tan = Rc sin /(R g Rc cos ). The distribution of galaxies in the Virgocentric reference frame {Vvc, Rvc} is represented in Fig. 3. Only the 391 galaxies with angles obeying < 45 or > 135 from the whole 2D sample are shown here. Selecting galaxies situated approximately in front and behind the cluster is meant to reduce the role of tangential velocity components, which are still unknown. The polygon curve traces the running median with a window of 1 Mpc. The median follows roughly the linear Hubble regression with H0 = 72 km s1 Mpc1 (the inclined dashed line) at middle Virgocentric distances of 15 Mpc, but tends to deviate from the H0 Rvc line at smaller scales, crossing the zero-velocity line at R0 6 Mpc. The behaviour of the running median at large scales is strongly skewed by a selection effect because of the adopted limit for galaxy velocities VLG < 3000 km s1. Another approach can also be used for converting the observational radial velocity of a galaxy Vg into its Virgocentric velocity (the case of pure Virgocentric flow; the Vf case). If the galaxy is not involved in the general cosmological expansion but is falling instead towards the Virgo cluster with a velocity Vin (Fig. 2b), then its radial velocity relative to the observer will be expressed as Vg = Vc cos and the infall velocity Vin itself can be written as Vin = (Vc cos Figure 2. Galaxy (G) motion with respect to the cluster centre (C) in the LG rest frame (top) in the case of almost pure Hubble flow and (bottom) in the case of almost pure Virgocentric infall. The angles and are shown in Fig. 2b. Evidently, the discrepancy between these two extreme approaches, the Hf and Vf cases, decreases when tends to 0 or to 180. As can easily be seen, selecting galaxies in the cone both with apex angle = 30 and with angle entails a loss of galaxies at large Virgocentric distances. This becomes apparent in the top-right corner of Fig. 3. A selection of galaxies in the volume Rvc < 30 Mpc (3D sample) reduces the bias appreciably. Fig. 4 represents the sky distribution of galaxies with known Virgocentric distances up to 30 Mpc in equatorial coordinates. The galaxies of this 3D sample are marked as circles and their diameters indicate three distance ranges: 012, 1222 and more than 22 Mpc from the observer. This map shows that the selection of galaxies by their angle < 30 brings some systematic skews dependent on distance. In particular, the foreground Virgo galaxies are preferentially removed by this angular selection. The Hubble diagram for 1792 galaxies of the 3D sample is represented in Fig. 5. The symbols for objects from different sources of distance data are the same as for Fig. 1. The number of galaxies in the 3D sample is roughly three times as large as in the 2D sample. It is worth noting that they populate the crucial regions in front and behind the Virgo cluster more thoroughly, giving us an opportunity for more detailed analyses of the Virgocentric infall. The velocity distance relation for these galaxies with respect to the cluster centre is shown in Fig. 6. The top panel corresponds to the assumption of pure Hubble flow of galaxies (the Hf case) while the bottom panel represents the case of pure radial motions towards the Virgo centre (the Vf case). As previously, the galaxies located far away from the line of sight crossing the cluster centre (i.e. with 45 < < 135) are eliminated in order to reduce the role of unknown tangential velocity components. This condition diminishes the number of sampled galaxies by 42 per cent. A comparison of the top and bottom panels of Fig. 6 shows that switching from the Hf case to the Vf case does not lead to any dramatic changes in the Hubble flow pattern given in the Virgocentric coordinates. Some galaxies move along the vertical axis appreciably but the total behaviour of the running medians traces the infall of galaxies towards the cluster in a similar way. The asymptotic tendency of the median at large distances Rvc looks much more regular for the 3D sample than for the 2D sample. Our elimination of galaxies with 45 < < 135 is slightly arbitrary. To estimate the response of the Virgocentric flow pattern to changing this condition, we have also imposed a more rigid constraint, eliminating galaxies with 30 < < 150. The corresponding diagrams for the Hf and Vf cases are represented in Fig. 7. As is seen, the more severe selection of galaxies by reduces their number by more than a half. However, the behaviour of the running median is almost the same. In the bottom panel of Fig. 7, every galaxy from samples iiv (see Table 1) having a distance error within 12 per cent is supplied by error bars indicating where the galaxy should be situated if its distance from the observer changes by 1 D. As expected, these error bars are much longer for galaxies situated behind the cluster. Changing a galaxy distance by 12 per cent, in some regions of the {Vvc, Rvc} diagram, leads to significant displacement of the galaxy along both Virgocentric coordinates, and therefore to appreciable galaxy skips relative to the zero-velocity line. (We do not include the longer error bars for the TullyFisher distances.) To quantify the uncertainties on the running median curves plotted in Figs 6 and 7, we generated extensive sets of bootstrap realizations. Their results permit us to estimate the radius of the zero-velocity surface and also its rms error presented in Table 2. Column 1 shows the size of the window for a running median, taken to be 0.8, 1.0 and 1.2 Mpc. Columns 2 and 3 show the mean radius of the zero-velocity surface R0 and its rms scatter obtained with regards to the assumptions on the pure Hubble flow (Hf case) and the pure Virgocentric flow (Vf case), respectively; here only four samples (iiv) with precise distance moduli were taken into account. Columns 4 and 5 show the same quantities for samples v and vi with TullyFisher distances. Columns 6 and 7 show the radii R0 and their errors for the total set of available data on galaxy distances. We discuss the interpretation of these different estimates of R0 in the next section. 4 D I S C U S S I O N A N D C O N C L U S I O N S We have analysed the available observational data on distances and radial velocities of galaxies in the wide surroundings of the Virgo cluster in order to study the Virgocentric infall. The main purpose of this paper is to determine the radius of the zero-velocity surface R0, which separates the cluster from the global cosmic expansion. By using this observational quantity, we are able to estimate the total mass of the Virgo cluster concentrated within R0 and compare it with the virial mass estimates corresponding roughly to a four times lower scale, Rvir. Based on the Hubble diagrams transformed into Virgocentric coordinates and the results of our bootstrap numerical experiments given in Table 2, we derive R0 to be in the range of 5.07.5 Mpc with a typical random error of 1.0 Mpc. The derived value of R0 can be affected by some systematic circumstances. The analysis of the Hubble diagrams in the Virgocentric coordinates suffers from a lack of data on the tangential velocity components of the galaxies. We tried to overcome this drawback with assumptions regarding a dominant type of galaxy motion in the proximity of Virgo. We performed a conversion of the observed radial velocities of galaxies into their Virgocentric velocities under two extreme kinematic assumptions: almost unperturbed Hubble flow (the Hf case) or almost pure radial flow towards Virgo (the Vf case). We found that adopting one or another scheme does not significantly change the general pattern of the Virgocentric infall. Calculating velocities in the Vf case yields, on average, some smaller values of Vvc, which causes a slightly larger (+0.7 Mpc) value of R0. The R0 quantities presented in Table 2 tend to be correlated with the smoothing window size. When the window changes from 0.8 to 1.2 Mpc, the radius decreases to 0.3 Mpc on average. Variation the window size in a wider range, from 0.5 to 2.0 Mpc, still leaves R0 within its random errors. The most noticeable systematic variations in the radius R0 are seen in dependence on galaxy samples. The use of samples of galaxies with only precise distance measurements (via Cepheids, TRGB, SBF and SNIa) yields the radius R0 within 6.57.5 Mpc, while the use of less precise TullyFisher distances leads to R0 estimates around 5.2 Mpc. The physical origin of this difference is clear. Probably, the instance is related to the fact that a typical distance error for the TullyFisher method (20 per cent) corresponds at the Virgo distance to a linear scale of 3.4 Mpc, comparable with the virial diameter of the cluster (3.6 Mpc). Large random errors can throw galaxies over the virial column, diluting the shape of the S-wave infall. Nevertheless, we should stress that two completely independent sets of observational data on distances to early-type Window (Mpc) 0.8 1.0 Primary distances (samples iiv) Hf 6.791.12 6.591.05 6.461.01 Vf 7.781.13 7.541.03 7.420.97 Hf Vf 5.071.04 4.870.88 4.710.78 5.581.13 5.380.97 5.240.87 All Hf 5.150.96 5.001.00 4.800.95 Vf 5.821.04 5.651.07 5.521.03 and late-type galaxies lead to compatible values of R0. As can be seen from Table 1, two samples with TullyFisher distances (v and vi) are about two times as large in galaxy number as the samples (iiv) with precise distances. Because we estimate R0 based on the running median without regard to galaxy weights (distance errors), the radius R0 for the total sample turns out to be closer to that for the former samples. Assuming R0 for the Virgo cluster in the range of (5.07.5) Mpc, we obtain from equation (4) the total mass of the cluster to be within MT = (2.78.9) 1014 M . This value is consistent with the virial mass estimates for the Virgo cluster: (5.5 1.4) 1014 M (Hoffman et al. 1980), (7.5 1.5) 1014 M (Tully & Shaya 1984) and 7.0 1014 M (Tonry et al. 2000) normalized to the same Hubble parameter H0 = 72 km s1 Mpc1. It should be remembered that this agreement is on very different scales as the zero-velocity radius, R0, is roughly four times as large as the virial radius. This means our results are consistent with there being no additional mass outside the virial radius of the Virgo cluster. Two items are worth mentioning in conclusion. The stated method of estimating the R0 value from observational data relies on the assumptions that a cluster has spherically symmetric shape and that galaxy motions around the cluster are regular without a significant tangential component. Deviations from the simple spherical infall scenario have been considered both theoretically and observationally by many authors (Peebles 1980; Davis & Peebles 1983; Lilje, Yahil & Jones 1986; Mould et al. 2000; Tonry et al. 2000; Watkins, Feldman & Hudson 2009). In particular, Tonry et al. (2000) studied a peculiar velocity field around the LG and the Virgo cluster in the presence of a second attractor (Great Attractor) situated in HydraCentaurus. As seen from their figs 20 and 21, the Great Attractor with a total mass of 9 1015 M , situated at a distance of 43 Mpc, generates significant distortions in the velocity field over an area of 1 steradian. Besides, Tully (1988) found the so-called effect of Local Velocity Anomaly arising by a push of the Local Void. According to Tully et al. (2009), a bulk motion of 260 km s1 toward the Supergalactic pole may be attributed to the Local Void. Recently, cosmic velocity flows in the Local Universe were also studied by Erdogdu et al. (2006), Haugbolle et al. (2007) and Lavaux (2009). We would emphasize that observational abilities to determine R0 and MT with better accuracy have not yet been exhausted. With the derived R0 around 7 Mpc, the zero-velocity surface is situated at a distance of about 10 Mpc from the observer (i.e. on the Local Volume edge). Hence, we can expect to find some number of LV galaxies with radial velocities (10002000) km s1, residing in front of Virgo. A new updated version of the CNG (Karachentsev et al., in preparation) contains about 40 candidate dwarf galaxies, such as VCC1675, with appropriate radial velocities and rough distance estimates. Their precise distances could be easily measured using the TRGB with the facilities of the ACS on the HST in the one-object-per-one-orbit mode. The addition of more galaxies with measured distances in the range 911 Mpc from the LG would allow a better measurement of R0. In particular, these galaxies could be used to better rule out the case where there is a large amount of mass outside the virial radius. This work was supported by RFBR 07-02-00005, RFBR-DFG 0602-04017 and CNRS grants. The authors thank Dmitry Makarov, Helene Courtois and Stefan Gottloeber for useful discussions. We would also like to thank the anonymous referees for their valuable comments, which led to significant improvements in the paper.

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I. D. Karachentsev, O. G. Nasonova. The observed infall of galaxies towards the Virgo cluster, Monthly Notices of the Royal Astronomical Society, 2010, 1075-1083, DOI: 10.1111/j.1365-2966.2010.16501.x